If you are getting that error, it means that you are opening the workbook that is on Tableau Public and not on your local machine. When you hover over an icon of your workbook on Tableau Desktop, it will show you the path where it is stored locally or on a server.
If the workbook was saved on Tableau Public, then you may have the workbook in your machine unless you have deleted that too. You may need to search for it.
I am using Tableau Desktop Public Edition 10.3
The situation is actually the reverse of what you mentioned - it is NOT on Tableau Public Online, but the .twbx workbook is on my machine.
I downloaded that .twbx workbook from Tableau Public Online previously, and after downloading it deleted the online version.
Now I'm trying to re-create the online version from the previously downloaded .twbx workbook, but the desktop app won't let me and returned that error.
What is the data source for the workbook? Can you share the downloaded workbook?
never mind. hacked it. found a workaround.
You can only open a twbx in Tableau Public if the viz is on Tableau Public. So, if you deleted it from Public and try to open a local copy, it won't work. Best solution is to download a trial version of the full Desktop client (or borrow one from someone), open the workbook, then resave to Tableau Public.